Linear Anti-windup Compensator Research Articles

Robust practical prescribed time trajectory tracking of USV with guaranteed performance

In this paper, a practical prescribed time tracking control scheme is proposed to drive the unmanned surface vehicle (USV) under input saturation and unknown disturbances to track the desired trajectory with guaranteed transient and steady-state performances. First, by employing the logarithmic type barrier Lyapunov function and prescribed time function, the virtual velocity law is designed at the kinematic level. Then, to deal with the unknown disturbances, a prescribed time observer is constructed to achieve perturbation attenuation in a user-defined time. Together with the linear anti-windup compensator, a robust trajectory tracking controller is constructed, which is capable of guaranteeing that all signals in the closed-loop system are uniformly ultimately bounded (UUB) and the tracking error converges to a user-defined compact set in predetermined time with prescribed transient performance. Finally, the effectiveness of the proposed control scheme is validated through Lyapunov theory and numerical studies.

Adaptive saturated control for spacecraft rendezvous and docking under motion constraints

This paper investigates the problem of position tracking and attitude synchronization for spacecraft rendezvous and docking with a tumbling target, in which kinematic couplings, unknown disturbances, motion constrains, and input saturation are considered. A novel artificial potential function (APF) is developed to encode both three-dimensional pose information and two-dimensional image information regarding path constraint and field of view constraint, respectively. By integrating the APF into the sliding mode technique, an adaptive control strategy is proposed to realize the arrival of the chaser at the docking port without any risk of collision or loss of target features. In addition, a linear anti-windup compensator is introduced to compensate for the input saturation effect. Uniformly ultimately bounded of the closed-loop system is guaranteed through Lyapunov analysis. A specific simulation scenario of docking with the defunct satellite Envisat is created to demonstrate the effectiveness and robustness of the proposed control strategy.

Saturated Adaptive Relative Motion Coordination of Docking Ports in Space Close-Range Rendezvous

An adaptive relative pose controller for docking ports of two uncertain spacecraft in autonomous rendezvous and docking is developed. A novel relative translational and rotational model represented in the chaser body-fixed frame is derived first based on the classical Newton–Euler equations. Based on the proposed model, a six-degrees-of-freedom adaptive control law is presented based on norm-wise estimations for the unknown parameters of two spacecraft to decrease the online computational burden. Meanwhile, an adaptive robust control input is designed by introducing an exponential function of states to improve the response performance with respect to the traditional adaptive robust control. Moreover, a linear antiwindup compensator is employed to ensure the bounded performance of the control inputs. The explicit tuning rules for designing parameters are derived based on the stability analysis of the closed-loop system. It is proved in Lyapunov framework that all closed-loop signals are always bounded and the pose tracking error ultimately converges to a small neighborhood of zero. Simulation results validate the performance of the proposed robust adaptive control strategy.

Anti‐windup for a class of partially linearisable non‐linear systems with application to wave energy converter control

This paper studies the anti-windup (AW) problem for a certain class of non-linear systems, in which the plant is globally quadratically stable and also partially linearisable by a suitably chosen non-linear feedback control law. Three types of AW compensators are proposed for this type of non-linear system: the first one is a non-linear extension of the popular linear internal model control (IMC) scheme; the second one has a similar structure to the IMC AW compensator yet is of reduced order and has entirely linear dynamics; and the third one is again a linear AW compensator, but can endow the closed-loop system with some sub-optimal performance properties. All three AW compensators are able to provide global exponential stability guarantees for the aforementioned class of systems. This work was inspired by a wave energy application whose dynamics fall into the class of systems studied in this study. Simulation results show the efficacy of the three AW compensators when applied to the wave energy application.

Anti-windup for NDI quadratic systems

This paper proposes an anti-windup design technique for systems which contain two sources of nonlinearity, namely actuator saturation and a quadratic nonlinearity in the plant state equation. It is shown how a nominal nonlinear dynamic inversion controller can be augmented with an anti-windup compensator of a form similar to that which is popular in linear anti-windup compensation. It is shown further how the free parameters of this compensator can be chosen, using linear matrix inequalities, in a way in which the region of attraction of the closed-loop compensated system is enlarged. A numerical example illustrates the effectiveness of the proposed technique.

An Internal Model Control Anti-Windup Scheme With Improved Performance for Input Saturation Via Loop Shaping

Proposed here is a new approach for synthesizing an internal model control (IMC) anti-windup (AW) compensator for a stable plant subject to input saturation. Built on the conventional IMC AW scheme, which preserves the stability robustness of the unconstrained system, the proposed linear AW compensator improves the performance of the constrained system. The analysis conducted through the loop decomposition of the AW system clearly reveals the impacts of the AW compensator on the closed-loop stability and performance. Loop shaping techniques are executed to design the AW compensator. The effectiveness of this approach is demonstrated using a numerical example.

Nonlinear Scheduled Anti-Windup Design for Linear Systems

The nonlinear L/sub 2/ anti-windup framework introduced in Teel and Kapor (1997) reduces the anti-windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched L/sub 2/ disturbances. In this note, based on the structure proposed in that previous paper, we provide a linear matrix ineqaulity (LMI) formulation of high-performance anti-windup design for control systems with linear asymptotically stable plants. In particular, we first give a linear quadratic-based formulation of linear anti-windup compensation, in terms of the solution of a set of (always feasible) LMI constraints. Then, we propose a nonlinear scheduling technique, where hysteresis switching among a family of linear gains is employed for performance improvement. Both design techniques are demonstrated on an academic example.

Antiwindup for stable linear systems with input saturation: An LMI-based synthesis

This paper considers closed-loop quadratic stability and L/sub 2/ performance properties of linear control systems subject to input saturation. More specifically, these properties are examined within the context of the popular linear antiwindup augmentation paradigm. Linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification, called the closed-loop behavior. Building on known results on H/sub /spl infin// and LPV synthesis, the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem, which has an attractive system theoretic interpretation: the lower bound on the achievable L/sub 2/ performance is the maximum of the open and unconstrained closed-loop L/sub 2/ gains. In the special cases of zero-order (static) and plant-order antiwindup compensation, the feasibility conditions become (convex) linear matrix inequalities. It is shown that, if (and only if) the plant is asymptotically stable, plant-order linear antiwindup compensation is always feasible for large enough L/sub 2/ gain and that static antiwindup compensation is feasible provided a quasi-common Lyapunov function, between the open-loop and unconstrained closed-loop, exists. Using the solutions to the matrix feasibility problems, the synthesis of the antiwindup augmentation achieving the desired level of L/sub 2/ performance is then accomplished by solving an additional LMI.